MCQMediumJEE Main 2024 · 4 April, Shift 2Limits

Mathematics Question from JEE Main 2024 · 4 April, Shift 2

Let f(x)f(x) = ∫0x(t+sin⁡(1−et)) dt\int_0^x \left(t + \sin(1 - e^t)\right) \, dt, x∈Rx \in \mathbb{R}. Find lim⁡x→0f(x)x3\lim_{x \to 0} \frac{f(x)}{x^3}:

  • A

    16\frac{1}{6}

  • B

    −16-\frac{1}{6}

  • C

    −23-\frac{2}{3}

  • D

    23\frac{2}{3}

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